Hans Andersen has been banned from two home meetings for Swindon because of a dispute over his availability.
The Dane has chosen to ride for home club Fjelsted on Wednesday instead of appearing for the Robins against King's Lynn - despite an agreement stating British fixtures take priority.
And the club confirmed the British Speedway Promoters' Association have handed the 32-year-old a suspension.
"He really should be here," Swindon boss Alun Rossiter told BBC Wiltshire.
"He's just become a Dad so that probably doesn't help matters but he should be here - that's the bottom line."
Andersen was part of the team who helped the Robins to the Elite League title last season and he was brought back to the club on loan from Peterborough for the 2013 campaign.
He was made captain by Rossiter, but the Swindon manager admits he may now reconsider his decision.
"It's something I will be looking at this week," said Rossiter.
"There's a little bit of hotness between the two parties. I think we need to cool down a bit so now is not the time, but we will address it [the captaincy]."
Andersen will miss Thursday's return fixture with King's Lynn as well as the home meeting against Wolverhampton on 11 July.
Chris Harris will guest for Swindon on Wednesday night against the Stars.